Phylogeny reconstruction BNFO 602 Roshan

Simulation studies

Software Random trees: r8s Sequence evolution: seqgen Tree comparison: recidcm3 software

Maximum Parsimony Character based method NP-hard (reduction to the Steiner tree problem) Widely-used in phylogenetics Slower than NJ but more accurate Faster than ML Assumes i.i.d.

Maximum Parsimony Input: Set S of n aligned sequences of length k Output: A phylogenetic tree T –leaf-labeled by sequences in S –additional sequences of length k labeling the internal nodes of T such that is minimized.

Maximum parsimony (example) Input: Four sequences –ACT –ACA –GTT –GTA Question: which of the three trees has the best MP scores?

Maximum Parsimony ACT GTTACA GTA ACA ACT GTA GTT ACT ACA GTT GTA

Maximum Parsimony ACT GTT GTA ACA GTA MP score = 5 ACA ACT GTA GTT ACAACT MP score = 7 ACT ACA GTT GTA ACAGTA MP score = 4 Optimal MP tree

Maximum Parsimony: computational complexity ACT ACA GTT GTA ACAGTA MP score = 4 Finding the optimal MP tree is NP-hard Optimal labeling can be computed in linear time O(nk)

Local search strategies Phylogenetic trees Cost Global optimum Local optimum

Local search for MP Determine a candidate solution s While s is not a local minimum –Find a neighbor s’ of s such that MP(s’)<MP(s) –If found set s=s’ –Else return s and exit Time complexity: unknown---could take forever or end quickly depending on starting tree and local move Need to specify how to construct starting tree and local move

Starting tree for MP Random phylogeny---O(n) time Greedy-MP

Greedy-MP takes O(n^2k^2) time

Local moves for MP: NNI For each edge we get two different topologies Neighborhood size is 2n-6

Local moves for MP: SPR Neighborhood size is quadratic in number of taxa Computing the minimum number of SPR moves between two rooted phylogenies is NP-hard

Local moves for MP: TBR Neighborhood size is cubic in number of taxa Computing the minimum number of TBR moves between two rooted phylogenies is NP-hard

Local optima is a problem

Iterated local search: escape local optima by perturbation Local optimum Local search

Iterated local search: escape local optima by perturbation Local optimum Output of perturbation Perturbation Local search

Iterated local search: escape local optima by perturbation Local optimum Output of perturbation Perturbation Local search